Setting Up Your First CP-SAT Model in OR-Tools

Learn to build a complete CP-SAT model in Python with OR-Tools: declaring integer and Boolean variables, adding linear constraints, setting an objective, invoking the solver, and reading back the optimal values.

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Tutorial

The CpModel Object and Decision Variables

A CP-SAT model is a Python object that holds decision variables, constraints, and (optionally) an objective function. We build one by importing the library and instantiating a $\texttt{CpModel}$ :

\begin{aligned}&\texttt{from ortools.sat.python import cp\_model} \\ &\texttt{model = cp\_model.CpModel()}\end{aligned}

To add an integer decision variable, call $\texttt{NewIntVar(lb, ub, name)}$ , where $\texttt{lb}$ and $\texttt{ub}$ are the inclusive integer lower and upper bounds, and $\texttt{name}$ is a string used in solver output:

\texttt{x = model.NewIntVar(0, 10, 'x')}

This declares a variable $x$ with domain $\{0, 1, 2, \ldots, 10\}.$ For Boolean variables (domain $\{0, 1\}$ ), use $\texttt{NewBoolVar(name)}$ instead:

\texttt{b = model.NewBoolVar('b')}

Every variable must be created by the same $\texttt{CpModel}$ instance that will later hold constraints referring to it. The argument order is always $(\texttt{lb}, \texttt{ub}, \texttt{name})$ — bounds first, name last.